The question is a bit general - are you looking for touristy stuff? Outdoors/animal/zoo stuff? Spa/pampering for your better half? Golf? Casino/gambling? Organized tour? Etc etc
Joburg is much like any other big city in the world, I guess with an African twist to it. If you're going to be hunting then the Joburg Zoo or the Lion Park just north of the city probably don't make much sense. Equally if you come from the US, then shopping is best done at home.
If you're looking for African trinkets etc to take home then there are a few (touristy) markets around the city. As far as culture goes, the Apartheid museum already mentioned is an option. There are a couple of 'cultural villages' (read African villages designed with the tourists $$$ in mind) round and about Joburg. Otherwise there are not that many real world famous landmarks in the city.
If you shed more light on what you're looking for, then I'd be happy to add my suggestions.